Chapter 8

Graphing Linear Equations

§8.1 – 2 Linear Equations in Variables

• What is an linear equation? What is a solution? 3x = 9

• What is an linear equation in 2 variables? What is a solution? 2x + y = 10

§8.1 – 2 Linear Equations inVariables

• Linear equations in 2 variables– Ordered pairs– Complete ordered pair given one of the values

• Rectangular coordinate system structure– Axes and quadrants– Plotting points– Determining coordinates of plotted points

§8.2 – Graphing Linear Equations

• Algorithm on p. 2851. Find 3 solutions2. Plot corresponding points3. Draw line thru points• If not straight – find your error

• Ex: Graph 3x + 2y = 12• x and y intercepts

§8.2 – Graphing Linear Equations

• Horizontal lines y = a

• Vertical lines x = b

• Problem #42 p. 290– Why only positive values?

§8.3 – The Slope of a Line

• What is slope?• Slope formula:

• General concepts– Positive slope– Negative slope– 0 slope– Undefined slope

2 1

2 1

y yriseslope m

run x x

§8.3 – The Slope of a Line

• Slope – intercept form:

• General concepts– y isolated– m is the slope– b is the y–intercept

y mx b

§8.3 – The Slope of a Line

• For each of the following lines, find the slope, the y–intercept, and graph the line

23 4y x

3 7 8x y

§8.3 – The Slope of a Line

• Parallel lines– What are they?– Same slope– Problems 8.3 #31, 32 (p. 297) – just parallel

• Perpendicular lines– What are they?– Slopes are negative reciprocals of each other– Problems 8.3 #31, 32 (p. 297) – just perpendicular

§8.4 – The Equation of a Line

• Slope – intercept form:

– Find equation given m and b• Problem 8.4 #22 (p. 301)

• Point – Slope form:

– Find equation given point and slope• Problem 8.4 #32 (p. 301)

– Find equation given 2 points• Problem 8.4 #52 (p. 301)

y mx b

1 1( )y y m x x